Let denote the Hermitian modular group of degree over an imaginary-quadratic number field . In this paper we determine its maximal discrete extension in , which coincides with the normalizer of . The description involves the -torsion subgroup of the ideal class group of . This group is defined over a particular number field and we can describe the ramified primes in it. In the case we give an explicit description, which involves generalized Atkin-Lehner involutions. Moreover we find a natural characterization of this group in .
Cite this article
Aloys Krieg, Martin Raum, Annalena Wernz, The maximal discrete extension of the Hermitian modular group. Doc. Math. 26 (2021), pp. 1871–1888DOI 10.4171/DM/859